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White is threatening mate (with Rxa6#), so black needs to check again (nothing that won’t lose a piece), block the rook (nothing except the Knight which would be taken or lead to a king move for a revealed check from the bishop). So that leaves Nc7 as the best course of action for black.

White would then move the king to set up a mate. Here’s what that line would look like from the start:1. Kf3, Nc7 2. Ke2+, Ka7 3. Qb6#

There might be some tricky counterplay that I’m missing like:1. Kf3, Rh3+ 2. Bxh3, Qh1+ 3. Bg2, Qxg2+ 4. Ke2, Qg4+ (To get the Queen over to the c8 square to defend). But I still think White comes out ahead since there’s a checking tempo on the black knight from the white queen combined with a mating threat.

There are only three moves at the start- Kf3, Kh4, and Rg6. On Kh4, black will mate starting with Qh7+; on Rg6, black will mate by playing Qg6 followed by either Qg4 or Qh6#. So, 1.Kf3 it must be:

1. Kf3

Now, black has her own problems. White is threatening Ra6#. If the knight moves to protect a6 from c7, white has a discovered check with Ke2: [1. …Nc7 2.Ke2 Re4 (or 2. …Rg2 3.Rd8+-) 3.Ra6 Na6 4.Qd5 Kb8 5.Qb5 Kc7 6.Qc6 Kd8 7.Be4 Qb2 8.Kf3 and black isn’t going to be able to save the knight and the rook at the same time.] Black could try the check from e4, but she still needs to deal with the Rxa6 threat, and this just puts her queen into danger: [1. …Qe4 2.Ke2 Qg4 3.Kd3 and black can’t protect a6 with the knight because it is pinned, and Qc8 is no good due to Bd5+ followed by mate.] I really don’t see any move that is close to holding for black, but maybe I am missing the best defense.